The study of tight focusing characteristics of azimuthally polarized vortex beams and the implementation of ultra-long super-resolved optical needle

Abstract

In this paper, the tight focusing characteristics of azimuthally polarized vortex beams are systematically investigated. The azimuthally polarized vortex beam can be decomposed into left-handed and right-handed circularly polarized (LHCP and RHCP) waves. It is found that the longitudinal components of LHCP and RHCP at the focal plane are equal in magnitude and opposite in phase. Thus, the total longitudinal field disappears because of the complete destructive interference. In contrast, there is almost no interference between the transverse components of LHCP and RHCP. Thus, the total transverse field is the incoherent superposition of them. Since the absolute values of the topological charges of LHCP and RHCP components are not equal, the transverse components of LHCP and RHCP will concentrate on the different areas at the focal plane. It is the reason for the orbit-induced localized SAM at the focal plane. Then, we compare the focal spot characteristics of the radially polarized beam and the azimuthally polarized beam with a first-order vortex. The advantages and disadvantages of them are discussed in detail, respectively.<br/>For the radially polarized beam, the central focal spot is mainly longitudinal component, and the sidelobe is mainly transverse component. For the azimuthally polarized vortex beam with <i>l</i>=1, the central focal spot is mainly LHCP component, and the sidelobe is mainly RHCP component. In both cases, the field distribution of the central spot is the same, and both show a distribution similar to the zero-order Bessel function. The situation of the sidelobe is different. The sidelobe of the radially polarized beam shows a distribution similar to the first-order Bessel function and the sidelobe of the azimuthally polarized vortex beam shows a distribution similar to the second-order Bessel function. Therefore, the sidelobe of the radially polarized beam is closer to the optical axis, resulting in a larger central focal spot size. On the other hand, the sidelobe of the radially polarized beam accounts for a much smaller proportion of the total energy compared with that of the azimuthally polarized vortex beam. So the sidelobe peak intensity of the radially polarized beam is lower. Finally, an optimal binary phase element is designed to obtain an ultra-long super-resolution optical needle. The transverse FWHM can achieve 0.391<i>λ</i> and the longitudinal FWHM can achieve 25.5<i>λ</i> using only 6 belts.